Question

qual a derivada de √x + 5

Answer 1

Olá ! 

note que : 

$\sqrt{x} =x^{ \frac{1}{2} }$


derivando ... 

$f(x) = \sqrt{x} +5\\\\f(x)=x^{ \frac{1}{2} }+5\\\\\\f(x)'= \frac{1}{2} .x^{ \frac{1}{2} -1}+0.5x^{0-1}\\\\f(x)'= \frac{1}{2}.x^{- \frac{1}{2} }+0\\\\f(x)'= \frac{1}{2}. \frac{1}{x^{ \frac{1}{2} }} \\\\f(x)'= \frac{1}{2} . \frac{1}{ \sqrt{x} } \\\\f(x)'= \frac{1}{2 \sqrt{x} } \\\\f(x)'=\frac{1}{2 \sqrt{x} }. \frac{ \sqrt{x} }{ \sqrt{x} } \\\\f(x)'=\boxed{\boxed{ \frac{ \sqrt{x} }{2x} }}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ok$